A Simple Method to Derive the Bistatic Tracking Radar System Formulas ألشتماق هعادالث ساداس التتبع الث ائي

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1 Al-Shaabi: A Simple Mehod o Deive he Bisaic Tacking Rada Sysem Fomulas A Simple Mehod o Deive he Bisaic Tacking Rada Sysem Fomulas Khalil Ibahim Ali Al-Shaabi College of Eleconics Engineeing Univesiy of Mosul Absac Bisaic Tacking Rada (BTR is an advanced mode of convenional Bisaic Rada (BR which is used fo age deecion. The pinciple of woking of BTR sysem is same as ha fo Mono Saic Tacking Rada (MTR, wih he diffeence ha he ansmie is apa fom he eceive, and hey opeae sepaaely and independenly. In his pape, he associaed equaions ha conol he BTR sysem opeaion, was deived in a simple manne. These equaions deemine he eceive and ansmie anenna posiions o keep hei lines of sigh mee a he age, beside he assuance of acking he age duing maneuveing. The opeaion of he sysem was explained and he simulaion pogam was made o chaaceize he opeaion of he sysem by using he deived equaions in his pape. Keywods: Bisaic Rada, Tacking, Rada طشيمت بسيطت ألشتماق هعادالث ساداس التتبع الث ائي خليل ابشا ين علي الششابي كليت ذست األلكتش باث خاهعت الو صل الخالصت اى ساداس التتبع الث ائي و رج هتمذم هي الشاداس الث ائي االعتياد الز يستخذم لكشف اال ذاف الد يت. اى طشيمت عول زا الشاداس تشب هي حيث الوبدذ طشيمدت عودل ساداس التتبدع االحداد ال الدت هدع هالحةدت اى الوشسدلت تكد ى بعيذة عي الوستمبلت تعوالى بشكل ه فصل عي بعض وا ف ساداس التتبع الث ائي. لمذ تن ف زا الب ث اشتماق الوعادالث الخاصدت بدشاداس التتبدع الث دائي للت فيدك بديي ه الدع ال ائيداث للوشسدلت الوسدتمبلت ب يدث تلتمد خطد ط االشدعت ل دز ال ائياث ع ذ ال ذف هع ضدواى اسدتوشاسالوتابعت لل دذف اء دام الو دا سة. تدن ت ضديع عودل دزا ال ةدام اعدذاد بش داهح تشبي لتوثيل عول ال ةام باستخذام الوعادالث الت تن الت صل الي ا ف زا الب ث. Received: Acceped:

2 Al-Rafidain Engineeing Vol.0 No. Mach Inoducion In geneal he bisaic Rada is a ada sysem in which he ansmie and he eceive ae sepaaed by a disance compaable o he age-o-eceive ange used fo age deecion, posiioning, and acking [1,].The Monosaic adas suffe fom counemeasues, such as jamming, and ani-adiaion weapons, while he bisaic adas have less vulneabiliy o counemeasues[3,4].this is because he counemeasues ae concenaed owad he ansmie which is fa fom he eceive ha is keeping he eceive ou of hea. The implemenaion of he bisaic ada is moe complex han he monosaic ada because i needs synchonizaion fo ime, fequency, and anenna posiioning [5]. Many eseaches have been made o solve hese poblems such as in efeences [6, 7, 8, 9]. In addiion, he equaion of bisaic ada is moe complex han ha of monosaic ada. This pape ineess wih Bisaic Tacking Rada (BTR, which is he mos complex mode of he bisaaic ada sysems. This ada is mosly used in miliay applicaions, especially fo ai defense unde he wafae envionmens, so ha, i has he highes echnology fo accuae opeaion. The bisaic ada equaion given by Skolnik [1], Willis [], and Schejbal [3], deemines he geneal bisaic ange equaion applied fo bisaic ada sysems. This equaion is no sufficien fo bisaic acking ada because i needs anenna (o spaial synchonizaion. In his pape, he sudy was concenaed o deive he equaions ha epesen he elaionships beween he ansmie anenna and he eceive anenna diecions o conol he movemen of he ansmie anenna elaive o he movemen of he acking eceive anenna o make he sysem wok compaibly. The pinciple of opeaion of he sysem is he mase-slave wih high communicaion channel. The eceive saion is he mase saion, which is equipped by he acking eceive, he daa pocessing, and conol unis, while ansmie saion is he slave which eceives he commands fom he eceive saion o see is anenna owad he age as shown in figue (1. Fig. (1 Bisaic ada saions and hei locaions The iniial daa of he age epesening he elevaion angle, he azimuh angle, and he ange of he age, ae given wih espec o he eceive saion. In he eceive, he infomaion will be pocessed by using he fomulas of opeaion of he BTR sysem ha will be deived lae, and he commands will send o he ansmie o see is anenna owad he age. Though he acking phase, he commands ae coninuously send o he ansmie o 030

3 Al-Shaabi: A Simple Mehod o Deive he Bisaic Tacking Rada Sysem Fomulas keep is anenna illuminaing he age. The iangulaion mehod was used o deive he BTR fomulas as explained lae.. Geomeical Chaaceisics In he bisaic ada whee he age, he ansmie, and he eceive ae sepaaed fom each ohe, and each one is fa fom ohes. Theefoe, he simples mehod o analyze he geomey of he sysem is he iangulaion mehod which convenional o deive angula elaionships beween pas of he sysem. In his mehod, he age, he ansmie, and he eceive make heads of a iangle as shown in figue (. In his figue, he heads of he iangle (T, R, and O epesen he ansmie, he eceive, and he age especively. O - D D T D b R Fig. ( Bisaic iangle geomey Fom figue (, he hee geomeical paamees which ae consideed as he souce vaiables ae: a. The ansmie-eceive anenna sepaaion: his is known as he Base Disance (D b, which epesens he disance beween ansmie and eceive. This disance mus be consan duing he opeaion of he sysem. b. The Tansmie-Tage-eceive disance (S: his disance is known as he Tiangulaion Disance which is epesened by he summaion of he ansmie-age disance (D, and he age-eceive disance (D. I depends on he age posiion, and i vaies due o he coninuous moving of he age. c. The Tansmie-Tage-Receive angle (Ф-Ф: his is he main paamee of he (BTR geomey ha gives he saisfacoy of sysem opeaion, and i is known as he Bisaic Angle. This angle is epesened by he inesecion of he ansmie-age sigh line, and he eceive-age sigh line. This angle equals he diffeence beween he ansmie and eceive anenna diecion angles ( -, and i deemines he iangulaion faco of he bisaic ada (F whee: F = sin (( - / (1 Fo eal bisaic chaaceisics and opeaion, his faco mus be in he ange of ( as shown in Fig.(3 [5]. The fomulas o obain values of (, and ae given in appendix A 031

4 Al-Rafidain Engineeing Vol.0 No. Mach 01 Fig. (3 Tiangulaion faco fo bisaic ada 3. Bisaic Fomulas and Geomey The ansmied signal eaches he eceive afe being efleced fom he age hough he bisaic (iangula pah beween ansmie-age-eceive. Since he disance beween ansmie and eceive is lage and each one of hem opeaes independenly, seveal paamees mus be aken ino accoun. The measued paamees ae consideed as pimay such as he base disance beween ansmie and eceive, he delay ime which is known as popagaion ime of he signal epesening he bisaic pah (disance,he eceive anenna diecion (including azimuh, and elevaion angles, wih espec o he eceive saion. The ohe paamees ae calculaed by using he (BTR fomulas o pefom opeaion of he sysem. The fomulas of (BTR ae defined in he plane of he iangle wih veices epesened by ansmie (T, eceive (R, and age (O. To simplify he deivaion of (BTR fomulas his appoach consides he pojecion of his iangle on he gound defined by he heads as ansmie (T, eceive (R, and he pojecion of age on he gound (P as shown in Fig.(4. Figue (4 shows ha, he pojecion of he age is ou of he line connecing he ansmie and he eceive as a geneal condiion because he age is mosly eihe o he lef o igh of his line. O n h = P =180- ψ T X 1 M X Fig.(4 Deailed Bisaic ada geomey 03 R

5 Al-Shaabi: A Simple Mehod o Deive he Bisaic Tacking Rada Sysem Fomulas The paamees of he (BTR and hei associaed fomulas ae defined as in he following: a. The ansmie-eceive disance (D b : his is he base disance which can be measued by using he navigaion mehod such as he Global Posiioning Sysem (GPS o deemine he locaions of ansmie and eceive saions. b. The ansmie-age-eceive disance: his is called he iangulaion disance, he pah lengh, o he bisaic pah which can be deemined by measuing he ime of aival (delay ime of he ansmied signal afe being efleced fom he age o each he eceive, and i is given as: S = T x C ( Whee (C is he speed of ligh, (T is he delay ime beween ansmied and eceived signal, and (S is he bisaic disance o he iangula disance which epesens he ansmie-age-eceive pah of he ay. The accuae mehod fo measuing he delay ime is by using (GPS iming signal o synchonize he iming opeaion beween ansmie and eceive saions. c. The eceive anenna diecion (ψ : his is he angle which epesens he diecion of he efleced signal fom he age o he eceive. This angle can be accuaely calculaed in eading he elevaion and azimuh angles fom he anenna posiioning mechanism, and using he fomula: ψ = cos -1 (cos cos (3 In his fomula (ψ epesens he diecion of eceive anenna owad he age, ( is he elevaion angle of he eceive anenna, and ( is he azimuh angle of he eceive anenna. Noe ha ( and angles can be aken diecly fom he posiioning mechanism of he eceive anenna. The deivaion of he eceive anenna diecion in equaion (3 is given in appendix A. d. The age-eceive disance (D : i epesens he disance beween he age and he eceive. This disance can be calculaed by using he following fomula 10, which is deived in appendix B: D S Db (4 ( S D cos( b e. The age-ansmie disance (D : i epesens he disance beween he age and he ansmie. This disance can be calculaed using he following fomula which is deived in appendix B: D S Db SDb cos( (5 ( S D cos( b f. Tansmie anenna diecion (ψ : i is he combinaion of azimuh and elevaion angles of he ansmie anenna. These angles can be calculaed accoding o he eceive anenna azimuh and elevaion angle. Theefoe he elevaion angle of ansmie anenna can be calculaed using he following fomula: D sin( sin 1 (6 S D 033

6 Al-Rafidain Engineeing Vol.0 No. Mach 01 And he azimuh angle of he ansmie anenna can be calculaed using he following fomula: sin 1 D cos( sin( ( S D cos( (7 Deivaion of equaions (6 and (7 is given in appendix C. The diecion of ansmie anenna (ψ can be calculaed in he same manne as used o deive he eceive anenna diecion fomula, which is given in appendix A. This diecion is given by he following fomula: ψ = cos -1 ( cos ( cos ( (8 4. Sysem Opeaion The scenaio of he sysem opeaion can be summaized by eceiving he iniial daa of he age, locking he age, and acking of he age. The locaions of he ansmie and eceive saions can be deemined by using GPS, o he conou maps fo he egion of opeaion, and fixed in he pos saion (Deecion Rada Saion. The pos saion povides daa of he age wih espec o he eceive and ansmie locaions including (ε, α, ε, α,d, D, and D b and send hem o he eceive saion, as iniial daa. These daa ae pocessed and examined in he compue of he sysem which exiss in he eceive saion. When he ansmie and eceive anennas ae dieced owad he age as shown in figue (5, he sysem sas opeaion and he ansmie illuminaes he age and he compue in he eceive will compae he measued daa wih he incoming daa fom he pos saion. The measued daa ae obained by eading he ansmie and eceive anenna posiions, and he ime delay beween he diec signal fom he ansmie o he eceive fo coheen eceive, o by using he GPS iming signal as efeence ime fo ansmi and eceive opeaion fo he noncoheen eceive. The ime delay (T povides he iangulaion disance (S beween Tansmie-Tage-Receive. As he lock signal exiss he eceive will coninue o ack he age and send commands (including ε and α o he ansmie, anenna o illuminae he age.duing he ack phase, he compue eads he posiion of he eceive anenna ( ε and α, and he ime delay, hen calculaes he iangulaion disance (S,and he ansmie anenna posiion ( ε and α by using he deived equaions. This commands ansfeed o he ansmie saion by using elecommunicaion sysem accuaely. R R O T R Fig.(5 Inesecion of ansmie and eceive anenna main lobs a he age. 034

7 Al-Shaabi: A Simple Mehod o Deive he Bisaic Tacking Rada Sysem Fomulas Simulaion Resuls To validae he poposed mehod of deiving he BTR sysem equaions and algoihm, we pesen he simulaion esuls o povide he uiliy of his mehod. In he simulaion, hee diffeen cases of he iniial infomaion abou he age wee aken. The fis check will be done by checking he value of he iangulaion faco ( F in equaion ( 1 o idenify he condiion of he BTR sysem whehe i is valid o no. If i is no valid, he sysem will ese, fo valid condiion he sysem will poceed o check he Lock On signal sae. If he lock signal is (1 he sysem will poceed and acking is pefomed fo he maneuveing age. If he lock signal is (0, he sysem will ese. The simulaion of he bisaic acking ada geomey was developed by using (MATLAB 7 pogam. The pogam was designed o povide he validiy of opeaion of he sysem befoe saing opeaions. Also he pogam can be used wih ineface o calculae he geomey duing he acking phase as much as he age is locked by he acking eceive. Duing he acking phase, he pogam calculaes he posiion of he ansmie anenna elaive o he posiion of he eceive anenna o make he cene lines of he ansmie and eceive anenna main lobs ineseced a he age and o keep he inesecion coninuous duing maneuveing of he age. The simulaion esuls fo such assumed condiions of he age ae lised in able (1. The flow cha shown in figue (6 illusaes he seps o compue he posiion of he ansmie anenna elaive o he posiion of he eceive anenna, Table (1 Simulaion esuls fo he BTR sysem Inpu Daa Oupu Daa ε α ε α D D Db Ф Ф F T S L saus deg deg deg deg Km Km Km deg deg μsec Km Valid valid X X X invalid 6. Accuacy and eo souces Fom able (1, i can be seen ha hee is no eo in he numeical calculaions of he sysem geomey, because he sysem akes he eal values of daa and use hem in he deived equaions o calculae he elaive ansmie anenna diecion (ie. ε, and α. The accuacy of he sysem depends on he accuacy of equipmens used in he implemenaion, and he 035

8 Al-Rafidain Engineeing Vol.0 No. Mach 01 eo is ceaed by he measuing equipmens, bu no fom he equaions applied in he numeical calculaions. The esulan eo appeas in he diecion of he ansmie anenna. To ovecome he effec of he esulan eo fom he sysem devices, he Half Powe Beam Widh (HPBW of he ansmie anenna mus be lage han ha of he eceive anenna o keep illuminaion on he moving age duing acking phase. Fo such sysem, he acceped value of eo is abou (1% - 5% depending on he accuacy of he sysem equipmens and coss. 7. Conclusion In his pape, he concep of bisaic acking ada was explained by using a ansmie and acking eceive. This pape was concenaed in he iangulaion mehod fo he deivaion of he bisaic acking ada fomulas in ode o solve he poblem of anenna diecion synchonizaion beween he ansmie and he eceive. The deived equaions in his pape wee examined sequenially by using MATLAB pogam, so his sequence could be applied in he sofwae implemenaion o conol he pocess of he sysem opeaion. The poposed iangulaion faco fo such BTR sysem could be aken in he ange ( as a special condiion fo he miliay applicaions. Applying his mehod can solve he poblem of geomey complexiy of he bisaic acking ada as well as simplify he conol opeaions, and synchonizaion beween ansmie and eceive anenna. In ohe wods his appoach can solve many difficulies in he pacical implemenaion and opeaion of his ype of ada sysem by using he elaionships beween he ansmie and eceive anenna posiions. Acknowledgemens The auho would like o hank D.Museeb M. Jasem, and D. Thaffe Al Neema, fo hei valuable commens, and suggesions. Refeences 1. Meil I. Skolnik : "Rada Handbook", 1970, pp ( N. J. Willis, and H., D., Giffihs : "Advances in Bisaic Rada", 007, pp( P.Bezousek, V. Schejbal : "Bisiic and Mulisaic Rada Sysems",Radioengineeing, Vol.17, No.3,Sep. 008, pp( NAWCWPNS-TP 8347: "Eleconic Waefae and Rada Sysem Engineeing Hand Book", 1999, pp( E. Hanle : "Suvey of bisaic and mulisaic ada", IEE poceedings, Vol.13, P.F, No. 7,Dec. 1986, pp. ( D.Maduasinghe and A.P. Shaw :"Tage Localizaion by Resolving he Time Synchonizaion Poblem in Bisaic Rada Sysems using Space Fas-Time Adapive Pocesso", EURASIP Jounal on Advance in Signal Pocessing, Vol. 009, pp( W.Q. Wang and J. Cai:" Anenna Diecing Synchonizaion fo Bisaic Synheic Apeue Rada Sysems.", IEEE Anenna and Wieless Popagaion Lees, Vol. 9, 010,pp( W. Q. Wang: " GPS-Based Time, and Phase Synchonizaion Pocessing fo Disibued SAR",IEEE Tansacion on Aeospace and Eleconic Sysems",Vol. 45, No. 3, July. 009, pp ( Aadil Volkwin: "Suiabiliy of a Commecial Sofwae Defined Radio Sysem fo Passive Coheen Locaion.", A disseaion Submied o he Depamen of Elecical 036

9 Al-Shaabi: A Simple Mehod o Deive he Bisaic Tacking Rada Sysem Fomulas Engineeing, Univesiy of Cape Tawn, In fulfillmen of equiemen fo degee of Mase of Science in Engineeing. May- 008, (chp Meill.I.Skolnik "Inoducion o Rada Sysems",1980, pp. ( Appendices Appendix A Deivaion of eceive anenna and ansmie anenna diecion fomulas: Fom he iangle (OPR in figue (4: OP = D sin (1 PR = D cos ( Fom iangle MPR MR = PR cos (3 Subsiuing he value of (PR fom equaion ( hen equaion (3 will be MR = D cos cos (4 Fom iangle OMR MR = D cos (5 Combining equaions (4 and (5 hen cos = cos cos (6 = cos -1 (cos cos (7 = (8 In he same manne he diecion of ansmie anenna fomula will be given as = cos -1 (cos cos (9 = (10 Appendix B Deivaion of eceive-age and ansmie-age disance fomulas: Fom he iangle (OMR in figue (4 Le OM = n, MR = X D = n + X N = D -X Fom iangle OMT Le MT = X 1 D = n + X 1 N = D X 1 Combining equaions ( and (4 hen D X 1 = D X Bu X 1 = D b X hen D (D b X = D X D D b + D b X X = D X (6 (7 D D b + D b X = D (8 By adding he em (D +D D o boh side of equaion (8 hen D + D D + D D b + D b X = D + D + D D (9 (D +D D b + D b X = D + D D (10 Bu D +D = S (11 S D b + D b X = D + D D (1 S D b = D + D D D b X (13 Bu X = D cos (14 Then S D b = D + D D D b D cos (15 S D b = D (D + D - D b cos (16 S D b = D (S - D b cos (17 S Db Theefoe D = (18 ( S Db cos The fomula fo he disance beween he ansmie and he age deived as following. 037 (1 ( (3 (4 (5

10 Al-Rafidain Engineeing Vol.0 No. Mach 01 D = S D (19 S Db D = S (0 ( S D cos Then D = S b Db SDb cos ( S D cos b Appendix C Deivaion of ansmie anenna elevaion and azimuh angles fomulas: Fom he iangle (OPR in figue (4 OP = D sin (1 PR = D cos ( Fom iangle OPT OP = D sin (3 PT = D cos (4 And D = S D (5 Then equaions (3 and (4 will be wien as OP = (S D sin (6 PT = (S D cos (7 Combining equaions (1 and (6 (S D sin = D sin (8 D sin sin = (9 S D D sin Then = sin 1 S D (10 Fom iangle PMR MP = PR sin (11 Subsiuing he value of PR fom equaion ( MP = D cos sin (1 Fom iangle MPT MP = PT sin (13 Subsiuing he value of PT fom equaion (7 hen MP = (S D cos sin (14 Subsiuing he value of MP fom equaion (1 hen (S D cos sin = D cos sin (15 D cos sin sin = ( S D cos (16 D cos sin = sin 1 ( S D cos (17 (1 The wok was caied ou a he College of Eleconics Engineeing Univesiy of Mosul 038

, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t

, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t Lecue 6: Fiis Tansmission Equaion and Rada Range Equaion (Fiis equaion. Maximum ange of a wieless link. Rada coss secion. Rada equaion. Maximum ange of a ada. 1. Fiis ansmission equaion Fiis ansmission